David Cameron has dismissed Labour calls for a rethink on government plans to impose cuts of 20% on the police as he addressed an emergency sitting of the House of Commons after the riots across England.

A bipartisan atmosphere in the Commons was briefly broken when the prime minister said that the cuts were "totally achievable" without reducing the number of frontline officers.

Cameron's remarks, which followed unease about the planned police cuts among ministers, came as he announced a series of measures in response to the "most appalling scenes" in English cities.

The prime minister said:

• Theresa May, the home secretary, would work with Iain Duncan Smith, the work and pensions secretary, to produce a cross-government action programme on gangs. This would be a "national priority". May would report to parliament in October amid evidence that gangs co-ordinated some of the attacks on the police and some of the looting.

• The treasury would be freeing up £10m from its reserve.

• The army could be used for guarding duties if there were a repeat of such widespread riots in order to free up police to deal with violence.

•Police would be given discretion to remove face masks from people on the street "under any circumstances where there is reasonable suspicion that they are related to criminal activity".

• Any homeowner or business person whose property was damaged would be able to seek compensation under the Riot Damages Act even if they were uninsured. The government would provide police with funds to ensure they could meet "legitimate claims".

• No "phoney human rights concerns" about publishing CCTV images of suspects involved in rioting would be allowed to "get in the way of bringing these criminals to justice".

• Ministers would work with the police and MI5 to assess whether it would be right to stop people communicating via social network sites "when we know they are plotting violence, disorder and criminality". Cameron said he had asked the police if they needed new powers in this area.

Cameron praised the bravery of the police but said: "What became increasingly clear earlier this week was that there were simply far too few police deployed on to the streets. And the tactics they were using weren't working.

"Police chiefs have been frank with me about why this happened. Initially the police treated the situation too much as a public order issue – rather than essentially one of crime."

The mostly quiet and sombre atmosphere in the house changed briefly when the prime minister dismissed a call from Ed Miliband to rethink 20% cuts on policing. The Labour leader's remarks came amid fears among ministers that the cuts could leave an "exposed flank".

But the prime minister dismissed these concerns as he mounted a robust defence of his plans.

"What we are saying: over the next four years we are looking for cash reductions in policing budgets. Once you take into account the fact there is a precept, that helps fund the police, [the actual cash reduction of 6% over the next four years] is totally achievable without any reductions in visible policing. A growing number of police chiefs are making that point.

"Today we still have 7,000 trained police officers in back office jobs. Part of our programme of police reform is about freeing up police for frontline duties. That is why I can make this very clear pledge to the house. At the end of this process of making sure our police budgets are affordable we will still be able to surge as many police on to the streets as we have in recent days in London, in Wolverhampton, in Manchester. I do think it is important people understand that."

The prime minister revived his pre-election concerns about a "broken society" as he said that one of the main lessons from the riots was that too many children grew up not knowing the differences between right and wrong.

"This is not about poverty, it's about culture. A culture that glorifies violence, shows disrespect to authority, and says everything about rights but nothing about responsibilities. In too many cases the parents of these children – if they are still around – don't care where their children are or who they are with, let alone what they are doing. The potential consequences of neglect and immorality on this scale have been clear for too long, without enough action being taken."

The fact that many children ended up in gangs would be the subject of renewed ministerial interest. The prime minister said: "At the heart of all the violence sits the issue of the street gangs. Territorial, hierarchical and incredibly violent, they are mostly composed of young boys, mainly from dysfunctional homes. They earn money through crime, particularly drugs, and are bound together by an imposed loyalty to an authoritarian gang leader. They have blighted life on their estates with gang-on-gang murders and unprovoked attacks on innocent bystanders.

"I want us to use the record of success against gangs in some cities like Boston in the USA and indeed the Strathclyde police in Scotland, who have done this by engaging the police, the voluntary sector and local government. I want this to be a national priority."

The prime minister dismissed the idea of holding an early independent inquiry as he said parliament should first take the lead in examining the riots.